Actually, scale is much simpler than you think:
1/x tells how much 1 unit on the paper is in the real world.
1/100 means 1 cm on paper = 100 cm in the real world = 1 m
1/20 means 1 cm on paper = 20 cm in the real world = 0.2 m
but you could also say 1 inch on paper = 20 inch in the real world

I guess in your case, you want 1/4 inch on paper = 1 foot in real world, right?
Just need to resolve the equation:
1/4 inch = 12 inch
1 inch = 48 inch
so the scale you're looking for is probably 1/48